- Email: [email protected]
Water filling of carbon nanotubes membranes: Porosity and temperature effects
Chemical Physics Letters 552 (2012) 84–87
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Water filling of carbon nanotubes membranes: Porosity and temperature effects Ana Claudia Kipper, Leandro Barros da Silva ⇑ Departamento de Física, Universidade Federal de Santa Maria, Av. Roraima, 1000, CEP 97105-900, Santa Maria, RS, Brazil
a r t i c l e
i n f o
Article history: Received 26 June 2012 In final form 20 September 2012 Available online 27 September 2012
a b s t r a c t A systematic investigation of water filling of carbon nanotubes is presented. By means of a molecular mechanics approach it is shown that water enters spontaneously into the nanotubes and fulfill them completely. The absorbed water forms single-file structure into narrow nanotubes and ice-like structures into larger nanotubes. The relation between the water occupation and the nanotube diameter is linear when ice-like ordering of water is present. It is found that the number of stored molecules decreases quadratically with the increase of temperature and for larger nanotubes a transition from ordered ice-like to liquid is observed when temperature reaches 330 K. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
2. Methodology
Water transport through carbon nanotube (CNT) channels has generated a lot of attention in the last few years due to the number of possible applications, such as water purification and desalination, drug delivery, ion transport and so on [1–11]. The interest has increased significantly as it has been shown that CNTs may act as fast fluid transporters [12,13]. This property is closely related to the behavior of water in confinement: it may form a single-file arrangement inside small diameter carbon nanotubes or assume an ice-like structure in larger nanotubes [14–16]. In fact, the enhanced flow can be attributed to the particular water ordering inside the CNTs where a decreasing of the number of hydrogen bonds per molecule and longer lifetime of these bonds are predicted [17,12,13]. Recently it has been proposed that the fast flow transport is due the existence of a depletion layer with reduced viscosity close to the CNT wall [18], although the definitive answer may need to consider also the nature of carbon–water interaction [19]. All studies agreed that the structure of water within the CNTs plays a crucial role on the ability of the nanotubes in conducting fluids. This evoke to question what are the main factors which lead the water molecules to a particular configuration within the CNTs. Despite previous efforts made to understand the underlying process [20,21], some questions are still open: how temperature influences the filling process? Is temperature a key factor on the maximum water load? In order to clarify these points, we propose the study of the dynamics of the filling process and the properties of the final states at different thermodynamics conditions.
The molecular mechanics simulations were carried out using GROMACS 4.5.2 package [22]. The systems consisted in CNTs bundles forming an infinite membrane, initially empty, in contact with two previously thermalised (500 ps) water reservoirs. Bundles of (10,0), (12,0), (14,0), (16,0) and (18,0) nanotubes with a length of 30 Å were used in the simulation. Cell dimensions were chosen to contain 16 nanotubes per unit cell, as showed in Figure 1. The periodicity in z axis (nanotube axis) was removed in order to avoid inter-reservoirs interactions. Table 1 lists the cell dimensions and the CNT radius. The simulation time comprised a total of 10 ns, with timestep of 2 fs, and data was collected every 2 ps. Temperature was controlled by velocity rescale thermostat, within the range 285–360 K. The interaction between carbon nanotubes and water are described in terms of a Lennard–Jones potential (LJ). The parameters CO and rCO are obtained from Lorentz–Berthelot mixing rule, where rC ¼ 0:385 nm and C ¼ 0:439 kJ/mol [23]. Simple-point charge (SPC) model was used for water [24]. The long range electrostatics and van der Waals interactions were treated by a plain cut-off of 8.5 Å. In all simulations, carbon atoms were kept frozen at their initial positions.
⇑ Corresponding author. E-mail address: [email protected] (L.B. da Silva). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.09.038
3. Results and discussions Initially the filling of CNTs was analyzed. Figure 2 shows that the water occupation of CNTs at 300 K increases non-linearly from the beginning of the simulation until the complete filling of the nanotubes, remaining roughly constant afterwards. It is shown in the inset of Figure 2 the fitting curves for water filling of (10,0), (12,0), (14,0), (16,0) and (18,0) CNTs bundles. The best fit is found to be a 4th order polynomial, which results in a filling rate varying
A.C. Kipper, L.B. da Silva / Chemical Physics Letters 552 (2012) 84–87
85
Figure 1. Unit cell used in simulations. (a) XY plane view and (b) YZ plane view. Carbon atoms are represented green spheres, while oxygen and hydrogen are red and white spheres, respectively. In (a) the first water reservoir was omitted for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Nanotubes considered in simulation. The radius refers to individual nanotube radius and cell dimensions are the dimensions of the whole unit cell. Nanotube
Radius (Å)
Cell dimensions (Å)
(10, 0) (12, 0) (14, 0) (16, 0) (18, 0)
3.91 4.70 5.48 6.27 7.05
44.90 38.81 51.12 44.34 57.33 49.64 63.72 55.18 69.85 60.40
cubically with time until the complete filling. As the CNTs are getting filled, the mobility of waters inside the cavity decreases, which, consequently, increases the time necessary to accommodate new molecules. Figure 3 illustrates the relationship between maximum capacity and CNT radius. It is observed a good linear fit of the maximum occupation for CNT radius greater than 4 Å. The reason of this threshold lies on the fact that in narrow nanotubes, such as (10,0) CNT, water forms a single-file ordering, while in larger tubes there is a different ordering, similar to ice structure. Furthermore, the linear dependence on the water capacity with the radius of the CNT’s contrasts with the observed in systems on larger scales
(microscopic or wider pores), where a dependence on the square of radius is expected. This is due the fact that, for the CNT studied in this Letter, confined water is always arranged in highly ordered tubular structures, with pentagonal, hexagonal or heptagonal cross sections. As a result, the number of molecules in the cross section does not depends on the available area of the CNT’s, but the radius itself. In order to understand the effect of temperature in water filling of CNTs we present in Figure 4 the average water occupation of CNT cavity as function of time. In all cases it is observed that the maximum occupation decreases quadratically as the temperature increases. In (10,0) CNTs, although, the maximum variation in average water population observed for this temperature range was 0.3 molecule, which is below the standard deviation of the average for these calculations of occupation (which is about 1.5 molecule). For (12,0) CNTs and thereafter, however, the occupation decreases significantly with the increasing of temperature. As seen in Figure 4b–d, it can be seen that the storage capacity of the CNTs decreases approximately 20% as temperature increases from 285 to 360 K. Nanotubes (16,0) are found to show a different behaviour when compared to the previous CNT’s. Filling curves comprises two separate groups, where curves for 285 and 300 K form one group, and curves for 330 and 360 K form the other group. This suggest that
Figure 2. Average number of water molecules per CNT inside the bundle at 300 K during time simulation. In the inset, a detail of the first 10 ps of the run and the corresponding fitting curves.
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Figure 3. Average occupation per CNT at 300 K as function of CNT radius.
water presents different properties at each temperature groups with a transition of state between them. In order to investigate this result, some further analysis of dynamics properties and temperatures within the range 300–330 K were carried on (Figure 4d). The autocorrelation function of dipole moments of the water molecules (ACF) within the (16, 0) CNTs and their mean square displacement (MSD) were investigated. The ACF is defined as i ðtÞi CðtÞ ¼ hpi ð0Þp , where pi is the water dipole momentum of the ip2
th molecule, and MSD is given by hjDrðtÞj2 i ¼ hjri ðtÞ r i ð0Þj2 i, where ri is the position of the i-th water molecule. Additionally, it is shown the variation of hydrogen-bond (HB) lifetime with temR perature, defined as s ¼ tdðtÞdt. Here, dðtÞ is a function that assigns 1 for an existing HB and 0 otherwise.
From Figure 5 it can be seen that water at 285 and 300 K have dynamic properties rather different to its bulk state at 300 K. The ACF of dipole momentum (Figure 5a) indicates that water into the CNTs forms a structure with dipoles frozen at its initial orientations for a long time. When temperature reaches 330 K, the dipoles lose their correlation after a relatively short time, in a qualitatively similar manner to bulk water at 300 K. In addition, Figure 5b shows the alterations in the MSD of water at (16,0) due to temperature increase. At 285 and 300 K, water exhibit nearly no mobility, indicating a static and compact structure like found in ice state. At 330 and 360 K, on the other hand, water within (16,0) CNTs presents notable mobility. Interestingly, water at (16,0) CNTs only present a diffusivity typical of its bulk state (300 K) when temperature is as high as 360 K. Further investigation for temperatures in the range 300–330 K indicates a transition state between highly ordered state (bellow 300 K) and a liquid state (above 330 K). This conclusion is supported by the mean-lifetime of the HB’s (Figure 5c), which shows that at temperatures higher than 325 K there is a sudden drop from 1.500 ps to 0.617 ps (in this model, bulk water at 300 K has s = 0.636 ps). The comparisons made with bulk water at 300 K are useful to illustrate that, when in confinement, water no longer exhibits its characteristic mobility and diffusivity. This behavior is only restored when temperature increases to values significantly higher to 300 K. Finally, it is observed that the condition of confinement into the CNTs allows water to be arranged in a compact ice-like structure even at temperatures up to 300 K. For this reason, the number of molecules able to fit the CNT cavity is larger than in other conditions, increasing the overall storage capacity of the nanotubes. The frozen state is broken only when temperature reaches values higher than 300 K (330 and 360 K, in this work). At that point, the mean square displacement of the molecules and the HB mean lifetime approximates to the observed for bulk water at room temperature. This suggest that the structure is
Figure 4. Average number of water molecules per CNT as function of time for (a) (10, 0) (b) (12, 0), (c) (14, 0) and (d) (16, 0) bundles. In the insets are shown the average water occupation as a function of the temperature.
A.C. Kipper, L.B. da Silva / Chemical Physics Letters 552 (2012) 84–87
87
Figure 5. (a) ACF of total dipole, (b) MSD of water molecules inside (16,0) CNT at various temperatures and (c) mean lifetime of HB. Bulk water properties at 300 K are used as reference values.
then much less compact than the observed in the previous case, and, consequently, a lower amount of water storage is expected. 4. Conclusions In this Letter, a molecular mechanics study on water filling of various CNTs bundles was presented. The results showed that the number of water molecules filling CNT’s depends directly on the CNT radius, with the notable exception for CNTs where this value is lower than 4 Å. This is a consequence of the pattern of arrangement into the cavity: in narrow nanotubes, water forms a singlefile structure, while in larger CNTs, water forms an ordered ice-like structure. Temperature influences the storage capacity of the nanotubes, which decreases quadratically with the increasing of temperature. This is especially notable in larger CNTs and it may be attributed to the transition from a compact ice-like structure (which occurs at lower temperatures) to a fluid-like structure, when temperature reaches higher values. Acknowledgements Authors acknowledge Brazilian agencies CAPES, CNPq and FAPERGS for funding, CPAD/UFSM and CENAPAD/UNICAMP for computer time.
References [1] C. Liu, Y. Lv, Z. Li, J. Phys. Lett. 136 (2012) 114506. [2] Y. Nakamura, T. Ohno, Chem. Phys. Lett. 539540 (2012) 123. [3] B. Xu, B. Wang, T. Park, Y. Qiao, Q. Zhou, X. Chen, J. Chem. Phys. 136 (2012) 184701. [4] A.A. Milischuk, B.M. Ladanyi, J. Phys. Lett. 135 (2011) 174709. [5] Y. Wang, Y.J. Zhao, J.P. Huang, J. Phys. Chem. B 115 (2011) 13275. [6] X.W. Meng, Y. Wang, Y.J. Zhao, J.P. Huang, J. Phys. Chem. B 115 (2011) 4768. [7] J. Goldsmith, C.C. Martens, Phys. Chem. Lett. 1 (2010) 528. [8] M.E. Suk, N.R. Aluru, J. Phys. Chem. Lett. 1 (2010) 1590. [9] J. Su, H. Guo, ACS Nano 5 (2010) 351. [10] D. Bucher, S. Kuyucak, Chem. Phys. Lett. 477 (2009) 207. [11] J. Martí, M.C. Gordillo, Chem. Phys. Lett. 354 (2002) 227–232. [12] S. Joseph, N.R. Aluru, Nano Lett. 8 (2008) 452. [13] G. Hummer, J.C. Rasaiah, J.P. Noworyta, Nature 414 (2001) 188. [14] Y. Maniwa et al., Chem. Phys. Lett. 401 (2005) 534. [15] R.J. Mashl, S. Joseph, N.R. Aluru, E. Jakobsson, Nano Lett. 3 (2003) 589. [16] W.H. Noon, K.D. Ausman, R.E. Smalley, J. Ma, Chem. Phys. Lett. 355 (2002) 445. [17] M.C. Gordillo, J. Mart, Chem. Phys. Lett. 329 (2000) 341. [18] T.G. Myers, Microfluid. Nanofluid. 10 (2011) 1141. [19] D. Mattia, Y. Gogotsi, Microfluid. Nanofluid. 5 (2008) 289. [20] A. Berezhkovskii, G. Hummer, Phys. Rev. Lett. 89 (2002) 064503. [21] K. Wu, B. Zhou, P. Xiu, W. Qi, R. Wan, H. Fang, J. Chem. Phys. 133 (2010) 204702. [22] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, J. Chem. Theory Comput. 4 (2008) 435. [23] J.H. Walther, R. Jaffe, T. Halicioglu, P. Koumoutsakos, J. Phys. Chem. B 105 (2001) 9980. [24] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, J. Hermans, Interaction models for water in relation to protein hydration, in: Intermolecular Forces, D. Reidel Publishing Co., 1981.
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Water filling of carbon nanotubes membranes: Porosity and temperature effects Ana Claudia Kipper, Leandro Barros da Silva ⇑ Departamento de Física, Universidade Federal de Santa Maria, Av. Roraima, 1000, CEP 97105-900, Santa Maria, RS, Brazil
a r t i c l e
i n f o
Article history: Received 26 June 2012 In final form 20 September 2012 Available online 27 September 2012
a b s t r a c t A systematic investigation of water filling of carbon nanotubes is presented. By means of a molecular mechanics approach it is shown that water enters spontaneously into the nanotubes and fulfill them completely. The absorbed water forms single-file structure into narrow nanotubes and ice-like structures into larger nanotubes. The relation between the water occupation and the nanotube diameter is linear when ice-like ordering of water is present. It is found that the number of stored molecules decreases quadratically with the increase of temperature and for larger nanotubes a transition from ordered ice-like to liquid is observed when temperature reaches 330 K. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
2. Methodology
Water transport through carbon nanotube (CNT) channels has generated a lot of attention in the last few years due to the number of possible applications, such as water purification and desalination, drug delivery, ion transport and so on [1–11]. The interest has increased significantly as it has been shown that CNTs may act as fast fluid transporters [12,13]. This property is closely related to the behavior of water in confinement: it may form a single-file arrangement inside small diameter carbon nanotubes or assume an ice-like structure in larger nanotubes [14–16]. In fact, the enhanced flow can be attributed to the particular water ordering inside the CNTs where a decreasing of the number of hydrogen bonds per molecule and longer lifetime of these bonds are predicted [17,12,13]. Recently it has been proposed that the fast flow transport is due the existence of a depletion layer with reduced viscosity close to the CNT wall [18], although the definitive answer may need to consider also the nature of carbon–water interaction [19]. All studies agreed that the structure of water within the CNTs plays a crucial role on the ability of the nanotubes in conducting fluids. This evoke to question what are the main factors which lead the water molecules to a particular configuration within the CNTs. Despite previous efforts made to understand the underlying process [20,21], some questions are still open: how temperature influences the filling process? Is temperature a key factor on the maximum water load? In order to clarify these points, we propose the study of the dynamics of the filling process and the properties of the final states at different thermodynamics conditions.
The molecular mechanics simulations were carried out using GROMACS 4.5.2 package [22]. The systems consisted in CNTs bundles forming an infinite membrane, initially empty, in contact with two previously thermalised (500 ps) water reservoirs. Bundles of (10,0), (12,0), (14,0), (16,0) and (18,0) nanotubes with a length of 30 Å were used in the simulation. Cell dimensions were chosen to contain 16 nanotubes per unit cell, as showed in Figure 1. The periodicity in z axis (nanotube axis) was removed in order to avoid inter-reservoirs interactions. Table 1 lists the cell dimensions and the CNT radius. The simulation time comprised a total of 10 ns, with timestep of 2 fs, and data was collected every 2 ps. Temperature was controlled by velocity rescale thermostat, within the range 285–360 K. The interaction between carbon nanotubes and water are described in terms of a Lennard–Jones potential (LJ). The parameters CO and rCO are obtained from Lorentz–Berthelot mixing rule, where rC ¼ 0:385 nm and C ¼ 0:439 kJ/mol [23]. Simple-point charge (SPC) model was used for water [24]. The long range electrostatics and van der Waals interactions were treated by a plain cut-off of 8.5 Å. In all simulations, carbon atoms were kept frozen at their initial positions.
⇑ Corresponding author. E-mail address: [email protected] (L.B. da Silva). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.09.038
3. Results and discussions Initially the filling of CNTs was analyzed. Figure 2 shows that the water occupation of CNTs at 300 K increases non-linearly from the beginning of the simulation until the complete filling of the nanotubes, remaining roughly constant afterwards. It is shown in the inset of Figure 2 the fitting curves for water filling of (10,0), (12,0), (14,0), (16,0) and (18,0) CNTs bundles. The best fit is found to be a 4th order polynomial, which results in a filling rate varying
A.C. Kipper, L.B. da Silva / Chemical Physics Letters 552 (2012) 84–87
85
Figure 1. Unit cell used in simulations. (a) XY plane view and (b) YZ plane view. Carbon atoms are represented green spheres, while oxygen and hydrogen are red and white spheres, respectively. In (a) the first water reservoir was omitted for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Nanotubes considered in simulation. The radius refers to individual nanotube radius and cell dimensions are the dimensions of the whole unit cell. Nanotube
Radius (Å)
Cell dimensions (Å)
(10, 0) (12, 0) (14, 0) (16, 0) (18, 0)
3.91 4.70 5.48 6.27 7.05
44.90 38.81 51.12 44.34 57.33 49.64 63.72 55.18 69.85 60.40
cubically with time until the complete filling. As the CNTs are getting filled, the mobility of waters inside the cavity decreases, which, consequently, increases the time necessary to accommodate new molecules. Figure 3 illustrates the relationship between maximum capacity and CNT radius. It is observed a good linear fit of the maximum occupation for CNT radius greater than 4 Å. The reason of this threshold lies on the fact that in narrow nanotubes, such as (10,0) CNT, water forms a single-file ordering, while in larger tubes there is a different ordering, similar to ice structure. Furthermore, the linear dependence on the water capacity with the radius of the CNT’s contrasts with the observed in systems on larger scales
(microscopic or wider pores), where a dependence on the square of radius is expected. This is due the fact that, for the CNT studied in this Letter, confined water is always arranged in highly ordered tubular structures, with pentagonal, hexagonal or heptagonal cross sections. As a result, the number of molecules in the cross section does not depends on the available area of the CNT’s, but the radius itself. In order to understand the effect of temperature in water filling of CNTs we present in Figure 4 the average water occupation of CNT cavity as function of time. In all cases it is observed that the maximum occupation decreases quadratically as the temperature increases. In (10,0) CNTs, although, the maximum variation in average water population observed for this temperature range was 0.3 molecule, which is below the standard deviation of the average for these calculations of occupation (which is about 1.5 molecule). For (12,0) CNTs and thereafter, however, the occupation decreases significantly with the increasing of temperature. As seen in Figure 4b–d, it can be seen that the storage capacity of the CNTs decreases approximately 20% as temperature increases from 285 to 360 K. Nanotubes (16,0) are found to show a different behaviour when compared to the previous CNT’s. Filling curves comprises two separate groups, where curves for 285 and 300 K form one group, and curves for 330 and 360 K form the other group. This suggest that
Figure 2. Average number of water molecules per CNT inside the bundle at 300 K during time simulation. In the inset, a detail of the first 10 ps of the run and the corresponding fitting curves.
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A.C. Kipper, L.B. da Silva / Chemical Physics Letters 552 (2012) 84–87
Figure 3. Average occupation per CNT at 300 K as function of CNT radius.
water presents different properties at each temperature groups with a transition of state between them. In order to investigate this result, some further analysis of dynamics properties and temperatures within the range 300–330 K were carried on (Figure 4d). The autocorrelation function of dipole moments of the water molecules (ACF) within the (16, 0) CNTs and their mean square displacement (MSD) were investigated. The ACF is defined as i ðtÞi CðtÞ ¼ hpi ð0Þp , where pi is the water dipole momentum of the ip2
th molecule, and MSD is given by hjDrðtÞj2 i ¼ hjri ðtÞ r i ð0Þj2 i, where ri is the position of the i-th water molecule. Additionally, it is shown the variation of hydrogen-bond (HB) lifetime with temR perature, defined as s ¼ tdðtÞdt. Here, dðtÞ is a function that assigns 1 for an existing HB and 0 otherwise.
From Figure 5 it can be seen that water at 285 and 300 K have dynamic properties rather different to its bulk state at 300 K. The ACF of dipole momentum (Figure 5a) indicates that water into the CNTs forms a structure with dipoles frozen at its initial orientations for a long time. When temperature reaches 330 K, the dipoles lose their correlation after a relatively short time, in a qualitatively similar manner to bulk water at 300 K. In addition, Figure 5b shows the alterations in the MSD of water at (16,0) due to temperature increase. At 285 and 300 K, water exhibit nearly no mobility, indicating a static and compact structure like found in ice state. At 330 and 360 K, on the other hand, water within (16,0) CNTs presents notable mobility. Interestingly, water at (16,0) CNTs only present a diffusivity typical of its bulk state (300 K) when temperature is as high as 360 K. Further investigation for temperatures in the range 300–330 K indicates a transition state between highly ordered state (bellow 300 K) and a liquid state (above 330 K). This conclusion is supported by the mean-lifetime of the HB’s (Figure 5c), which shows that at temperatures higher than 325 K there is a sudden drop from 1.500 ps to 0.617 ps (in this model, bulk water at 300 K has s = 0.636 ps). The comparisons made with bulk water at 300 K are useful to illustrate that, when in confinement, water no longer exhibits its characteristic mobility and diffusivity. This behavior is only restored when temperature increases to values significantly higher to 300 K. Finally, it is observed that the condition of confinement into the CNTs allows water to be arranged in a compact ice-like structure even at temperatures up to 300 K. For this reason, the number of molecules able to fit the CNT cavity is larger than in other conditions, increasing the overall storage capacity of the nanotubes. The frozen state is broken only when temperature reaches values higher than 300 K (330 and 360 K, in this work). At that point, the mean square displacement of the molecules and the HB mean lifetime approximates to the observed for bulk water at room temperature. This suggest that the structure is
Figure 4. Average number of water molecules per CNT as function of time for (a) (10, 0) (b) (12, 0), (c) (14, 0) and (d) (16, 0) bundles. In the insets are shown the average water occupation as a function of the temperature.
A.C. Kipper, L.B. da Silva / Chemical Physics Letters 552 (2012) 84–87
87
Figure 5. (a) ACF of total dipole, (b) MSD of water molecules inside (16,0) CNT at various temperatures and (c) mean lifetime of HB. Bulk water properties at 300 K are used as reference values.
then much less compact than the observed in the previous case, and, consequently, a lower amount of water storage is expected. 4. Conclusions In this Letter, a molecular mechanics study on water filling of various CNTs bundles was presented. The results showed that the number of water molecules filling CNT’s depends directly on the CNT radius, with the notable exception for CNTs where this value is lower than 4 Å. This is a consequence of the pattern of arrangement into the cavity: in narrow nanotubes, water forms a singlefile structure, while in larger CNTs, water forms an ordered ice-like structure. Temperature influences the storage capacity of the nanotubes, which decreases quadratically with the increasing of temperature. This is especially notable in larger CNTs and it may be attributed to the transition from a compact ice-like structure (which occurs at lower temperatures) to a fluid-like structure, when temperature reaches higher values. Acknowledgements Authors acknowledge Brazilian agencies CAPES, CNPq and FAPERGS for funding, CPAD/UFSM and CENAPAD/UNICAMP for computer time.
References [1] C. Liu, Y. Lv, Z. Li, J. Phys. Lett. 136 (2012) 114506. [2] Y. Nakamura, T. Ohno, Chem. Phys. Lett. 539540 (2012) 123. [3] B. Xu, B. Wang, T. Park, Y. Qiao, Q. Zhou, X. Chen, J. Chem. Phys. 136 (2012) 184701. [4] A.A. Milischuk, B.M. Ladanyi, J. Phys. Lett. 135 (2011) 174709. [5] Y. Wang, Y.J. Zhao, J.P. Huang, J. Phys. Chem. B 115 (2011) 13275. [6] X.W. Meng, Y. Wang, Y.J. Zhao, J.P. Huang, J. Phys. Chem. B 115 (2011) 4768. [7] J. Goldsmith, C.C. Martens, Phys. Chem. Lett. 1 (2010) 528. [8] M.E. Suk, N.R. Aluru, J. Phys. Chem. Lett. 1 (2010) 1590. [9] J. Su, H. Guo, ACS Nano 5 (2010) 351. [10] D. Bucher, S. Kuyucak, Chem. Phys. Lett. 477 (2009) 207. [11] J. Martí, M.C. Gordillo, Chem. Phys. Lett. 354 (2002) 227–232. [12] S. Joseph, N.R. Aluru, Nano Lett. 8 (2008) 452. [13] G. Hummer, J.C. Rasaiah, J.P. Noworyta, Nature 414 (2001) 188. [14] Y. Maniwa et al., Chem. Phys. Lett. 401 (2005) 534. [15] R.J. Mashl, S. Joseph, N.R. Aluru, E. Jakobsson, Nano Lett. 3 (2003) 589. [16] W.H. Noon, K.D. Ausman, R.E. Smalley, J. Ma, Chem. Phys. Lett. 355 (2002) 445. [17] M.C. Gordillo, J. Mart, Chem. Phys. Lett. 329 (2000) 341. [18] T.G. Myers, Microfluid. Nanofluid. 10 (2011) 1141. [19] D. Mattia, Y. Gogotsi, Microfluid. Nanofluid. 5 (2008) 289. [20] A. Berezhkovskii, G. Hummer, Phys. Rev. Lett. 89 (2002) 064503. [21] K. Wu, B. Zhou, P. Xiu, W. Qi, R. Wan, H. Fang, J. Chem. Phys. 133 (2010) 204702. [22] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, J. Chem. Theory Comput. 4 (2008) 435. [23] J.H. Walther, R. Jaffe, T. Halicioglu, P. Koumoutsakos, J. Phys. Chem. B 105 (2001) 9980. [24] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, J. Hermans, Interaction models for water in relation to protein hydration, in: Intermolecular Forces, D. Reidel Publishing Co., 1981.